Two-dimensional nonlinear dynamics of beam–plasma instability

In continuation of previous work, numerical results are presented, concerning relativistically counter-streaming plasmas. Here, the relativistic mixed mode instability evolves through, and beyond, the linear saturation -well into the nonlinear regime. Besides confirming earlier findings, that wave power initially peaks on the mixed mode branch, it is observed that, during late time evolution wave power is transferred to other wave numbers. It is argued that the isotropization of power in wavenumber space may be a consequence of weak turbulence. Further, some modifications to the ideal weak turbulence limit is observed. Development of almost isotropic predominantly electrostatic -partially electromagnetic -turbulent spectra holds relevance when considering the spectral emission signatures of the plasma, namely bremsstrahlung, respectively magneto-bremsstrahlung (synchrotron radiation and jitter radiation) from relativistic shocks in astrophysical jets and shocks from gamma-ray bursts and active galactic nuclei.Counter-streaming plasmas subject to the relativistic mixed mode instability (MMI), driven by relativistic beams of electrons and ions, have previously been examined theoretically [1, 2], and numerically with particle-incell (PIC) simulations [3,4]. Growth rates of the mixed mode, the filamentation and the two-stream instabilities (hereafter MMI, FI and TSI, resp.), areand background plasma density, the beam speed and beam bulk Lorentz factor, respectively, in the background rest frame. For a large volume in parameter space, V ∈ {n b , n p , v b , Γ(v b )}, the MMI will have the highest growth rate of the three possible instabilities for the relativistic beam-plasma interaction. The MMI propagates at oblique angles with respect to the beam velocity Due to its mixed nature, the MMI contains both an electrostatic and an electromagnetic wave component [2]. Potentially, both electrostatic and electromagnetic turbulence (wave mode coupling leading to cascades/inverse cascades in k-space) is possible in such systems. This potential for producing very broad band plasma turbulence (in both E and B fields) is highly relevant when considering for example inertial confinement fusion experiments [5,6]. Other examples where electromagntic wave turbulence is important are astrophysical jets and shocks from gamma-ray bursts and active galactic nuclei, where ambient plasma streams through a shock interface moving at relativistic speeds -see e.g. [7,8,9]. Further studying of the MMI in particular, here, beyond the linear regime to the development of turbulence is thus highly motivated.Performing high resolution 2.5D PIC code simulations, we examine the turbulent wave spectra, that develop during saturation of the MMI by the trapping of electrons [3,4]. The code solves Lorentz' equations of motion for an ensemble of computational macro-particles (CPs) defined in 2D3V; {x, y, p x , p y , p z , t}, and Maxwell's equations in two spatial dimensions; {E x,y , B z }(x, y, t). A PIC code scaling is chosen wherein m e = e = c ≡ 1 f...

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“…the non-relativistic limit [10]. Our simulations -on the other hand -fully resolve all particle and wave dynamics.…”

mentioning

confidence: 64%

Electromagnetic turbulence driven by the mixed mode instability

Frederiksen¹,

Dieckmann

2008

Physics of Plasmas

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“…Thus, numerical analyses were carried out in one or two dimensional systems, such as in Refs. [21][22][23][24][25][26][27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Weak turbulence theory for collisional plasmas

et al. 2016

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Plasma is an ionized gas in which the collective behavior dominates over the individual particle interactions. For this reason, plasma is often treated as collisionless or collision-free. However, the discrete nature of the particles can be important, and often, the description of plasmas is incomplete without properly taking the discrete particle effects into account. The weak turbulence theory is a perturbative nonlinear theory, whose essential formalism was developed in the late 1950s and 1960s and continued on through the early 1980s. However, the standard material found in the literature does not treat the discrete particle effects and the associated fluctuations emitted spontaneously by thermal particles completely. Plasma particles emit electromagnetic fluctuations in all frequencies and wave vectors, but in the standard literature, the fluctuations are approximately treated by considering only those frequency-wave number regimes corresponding to the eigenmodes (or normal modes) satisfying the dispersion relations, while ignoring contributions from noneigenmodes. The present paper shows that the noneigenmode fluctuations modify the particle kinetic equation so that the generalized equation includes the Balescu-Lénard-Landau collision integral and also modify the wave kinetic equation to include not only the collisional damping term but also a term that depicts the bremsstrahlung emission of plasma normal modes.

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“…Figure 1 shows the time evolution of electron velocity distribution function by plotting F e in 2D velocity space at different time steps corresponding to ω pe t = 500, 1000, 2000, 5000, 10 4 , 1.5 × 10 4 , and 2 × 10 4 . The lefthand panels depict solutions with only collisions; the middle panels correspond to the self-consistent solution without collisional effects, as in the type III beam case (Ziebell et al 2008); and the righthand panels show solutions that contain both collisional effects and self-consistent Langmuir wave dynamics. As the lefthand panels show, the collisional relaxation of the beam leads to the systematic energy losses and isotropization of the beam.…”

Section: Numerical Analysismentioning

confidence: 99%

“…We considered the influence of Coulomb collisions and the self-consistent collective effects in the electron beam-plasma interaction problem in 2D velocity space. In the past, the present authors investigated the electron-Langmuir wave collective dynamics, which is relevant to the type III burst electrons, by ignoring the effects of Coulomb collisions (Ziebell et al 2008). On the other hand, early works on solar X-ray emission ignored the collective dynamics and only considered collisional dynamics.…”

Section: Final Remarksmentioning

confidence: 99%

“…Unlike previous works related to this type of analysis where the effects of Coulomb collisions have normally been ignored (Ziebell et al 2008), the present paper includes electron-electron and electron-ion collisions. On the other hand, unlike the previous works related to the solar X-ray problem where, in addition to collisional effects, quasilinear effects are included considering one-dimensional (1D) wave excitation, we now consider the nonlinear dynamics associated with the wave scattering and decay in two dimensions, along with the collisional dynamics.…”

Section: Introductionmentioning

confidence: 99%

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Two-dimensional time evolution of beam-plasma instability in the presence of binary collisions

Tigik

Ziebell

Yoon

et al. 2016

A&A

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Energetic electrons produced during solar flares are known to be responsible for generating solar type III radio bursts. The radio emission is a byproduct of Langmuir wave generation via beam-plasma interaction and nonlinear wave-wave and wave-particle interaction processes. In addition to type III radio bursts, electrons traveling downwards toward the chromosphere lead to the hard X-ray emission via electron-ion collisions. Recently, the role of Langmuir waves on the X-ray-producing electrons has been identified as important, because Langmuir waves may alter the electron distribution, thereby affecting the X-ray profile. Both Coulomb collisions and wave-particle interactions lead electrons to scattering and energy exchange that necessitates considering the two-dimensional (2D) problem in velocity space. The present paper investigates the influence of binary collisions on the beam-plasma instability development in 2D in order to elucidate the nonlinear dynamics of Langmuir waves and binary collisions. The significance of the present findings in the context of solar physics is discussed.

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Two-dimensional nonlinear dynamics of beam–plasma instability

Cited by 64 publications

References 30 publications

Electromagnetic turbulence driven by the mixed mode instability

Electromagnetic turbulence driven by the mixed mode instability

Weak turbulence theory for collisional plasmas

Two-dimensional time evolution of beam-plasma instability in the presence of binary collisions

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